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The difference of any two sides of a triangle is __ than the third side.

A carpenter had to make a triangle with sides 5, 6, 5 units. By mistake he made one with sides 5, 8, 5 units. The difference between their areas is:

The density of Ne is maximum at:

Question 16
If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation:

A) Changes
B) Remains the same
C) Only changes in case of multiplication
D) ​​​​​​​Only changes in case of division​​​​​​​

A line segment $AB$ is of length $5cm.$ Draw a circle of radius $4cm$ passing through $A$ and $B.$ Can you draw a circle of radius $2cm$ passing through $A$ and $B$? Give reason in support of your answer.

Meena needs to serve mango juice to her guests in cylindrical tumblers of radius 7 cm up to a height 10 cm. If she wants to serve 25 guests, how much juice does she need to prepare?

In the given figure, AB = AC, AD = AE = 5 cm and DC = 8 cm. Length of EB is.

Let $\varphi (x,y)=0$ be the equation of a circle, If $\varphi (0,\lambda )=0$ has equal roots $\lambda =2,2$ and $\varphi (\lambda ,0)=0$ has roots $\lambda =\frac{4}{5},5,$ then the roots of the circle is

The curved surface area of a right circular cylinder of height 7 cm is 44 cm², the diameter of the base of the cylinder is

A right angled triangle of which the sides containing the right angle are 6.3 cm and 10 cm in length,is made to turn round on the longer side.Find the volume of the solid,thus generated.Also,find its curved surface area.

If a² + b² + c² - ab - bc - ca = 0 then which of following is true.

In the formula for mode of a grouped data ,

$Mode=l+\left[\frac{f_1-f_0}{2f_1-f_0-f_2}\right]\times h$ ,

where symbols have their usual meaning, $f_1$ represents:

In the given figure, ABCD is a rhombus. If OB = 3 units, OC = 4 units and AE = 6.4 units. Find the length of BE.

When two unequal diagonals bisect each other at 90 degrees then, which quadrilateral we can construct?

In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.

If a + b + c = 9 and ab + bc + ca = 26, find the value of $a^3+b^3+c^3-3abc$.

Question 107

Music CD originally priced at Rs. 120 is on sale for 25 % off. What is the SP?
Sonia and Rahul have different ways of calculating the sale price for the items they bought.
As you work on the next problem, try both of these methods to see which your refer.

Construct a triangle ABC such that BC = 6 cm, AB = 6 cm and median AD = 4 cm.

In the given figure, the chord AB of the larget of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.

If we subtract $\frac{1}{2}$ from a number and multiply the result by $\frac{1}{2}$, we get $\frac{3}{8}$. Then the number is ___.

Ram has a plot of land of the shape of a quadrilateral. Government wants to take some portion of his land to build a hospital. Ram agrees with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented. [4 MARKS]

Find the value of $27x^3+8y^3$, if

(i) 3x + 2y = 14 and xy = 8

(ii) 3x + 2y = 20 and xy = $\frac{14}{9}$

The curved surface area of right circular cone whose slant height is 10 cm and base radius is 7 cm

If x:y::3:5, find the ratio 4x+9y:8x+9y.

Two planes intersect each other to form a:

Find the equation of straight line which passes through the point (3, 4) and sum of its intercepts on the x and y axis is 14

As shown in above figure AB and CD are two parallel lines and a line XY passes through them and intersects AB at P & CD at Q. If $\angle DQX=x^{\circ }$ then $\angle APY=$ ___.

In parallelogram ABCD if $\angle A=(3x-{20}^{\circ }),\angle B=(y+{15}^{\circ }),\angle C=(x+{40}^{\circ })$, then find the value of x and y .

Factorize : $x^4+x^2+25.$

In the adjoining figure,$△ABC$ and $△DBC$ are on the same base BC with A and D on opposite sides of BC such that $\left(△ABC\right)=ar\left(△DBC\right)$ Show that BC bisects AD.

Find the value of ‘k’ if x -1 is a factor of P(x) = 4$x^3$ + $x^2$ – 3x + k.

The value of $\frac{3}{5}\times (\frac{35}{24}+\frac{10}{1})$ is _____.

lf all the particles of a system lie in X-Y plane, is it necessary that the centre of mass be in X-Y plane?

From the options, choose the irrational numbers that lie between 4 and 9.

ABCD is a quadrilateral in which AD = BC. If P, Q, R, S be the midpoints of AB, AC, CD and BD respectively, show that PQRS is a rhombus.

If the point P(5, k-2) lies on the line $x-2y+1=0$, then find the value of k.

$\text{In}△ABC,\angle C={60}^{\circ }\text{and}\angle C>\angle B.\text{Which is the longest side of the triangle?}$

Consider the following two statements:
Statement - 1: If two figures have same shape and same size then they are called congruent.
Statement - 2: If two figures have equal area they are called congruent.
Now, choose the correct option.

What is the full form of W.R.T?

7 composite numbers between two consecutive prime numbers less than 100 are -

The value of $3\sqrt{54}÷2\sqrt{2}$ is

Question 41

In the following question, fill in the blanks to make the statements true.

Very large lumbers can be expressed in standrad from using ___ exponents.

A boy on a cliff 480 m high drops a stone. One second later he throws a second stone after the first. They both hit the ground at the same time. With what speed does he throw the second stone? (Take g=10m/s²).

The distance between the points $4\frac{1}{2}$ and $3\frac{1}{4}$ on the number line is

In a circular motion, the direction of velocity at any point is along the __.